In this work, we delve into geometric analysis, particularly examining the interplay between lower bounds on Ricci curvature and specific functionals. Our exploration begins with an investigation into the implications of Yamabe invariants for asymptotically Poincaré-Einstein manifolds and their conformal boundaries under conditions of $Ric\geq -(n-1)g$. We establish a relationship wherein the type II Yamabe invariant of the conformal compactification of the manifold is bounded below by the Yamabe invariant of its conformal boundary. Additionally, we focus on compact manifolds with boundary where $Ric\geq 0$ and $II\geq 1$, obtaining partial results concerning Wang's conjecture.
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